Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
418 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 16. #4699 | C4 | semidirect |
| 19. #4682 | C4 | semidirect |
| 20. #4681 | C4 | semidirect |
| 258. C3 | #9763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78475 | 2 |
| C3×#1726 | 2 |
| #69801 | 2 |
| #69732 | 2 |
| #69433 | 2 |
| #9763 | 3 |